# Course Modules for First Year B.A. Mathematics

## MODULE CODE: MH4731

## MODULE TITLE: Elementary Number Theory

## PREREQUISITE MODULE(S): None

## OBJECTIVES:

Number theory is a foundational branch of mathematics. This module gives the student a solid grounding in the subject.

## LEARNING OUTCOMES:

Students who successfully complete this module should be able to:

- understand the basic elements of number theory;
- understand notation and conventions associated with the topic;
- use known algorithms to solve problems related to divisibility;
- master modular arithmetic;
- produce coherent and convincing arguments;
- communicate solutions to problems clearly and coherently.

## MODULE CONTENT:

- Representations of numbers;
- The binomial theorem; Mathematical induction;
- Divisibility of integers; Prime Numbers and The Fundamental Theorem of Arithmetic;
- Euclid's algorithm
- Congruence; linear Diophantine equations; Fermat's Little Theorem; Using congruences to solve more complex problems;
- Pythagorean Triples.

## PRIME TEXTS:

ORE, O. (1969). Invitation to Number Theory. Mathematical Association of America.

SILVERMAN , J. H. (2012). A Friendly Introduction to Number Theory. Pearson Education.

## OTHER RELEVANT TEXTS:

NIVEN, I.M., ZUCKERMAN, H.S. (1980). An introduction to the theory of numbers, Wiley.

DUDLEY, U. (2008). Elementary Number Theory, Dover.

BURN, R.P. (1997). A pathway into number theory, Cambridge University Press.

FORMAN, S., RASH, A. (2015). The Whole Truth About Whole Numbers, Springer.

<<Previous Page (Outline Content)

## MODULE CODE: MH4722

## MODULE TITLE: Introduction to Geometry

## PREREQUISITE MODULE(S): None

## OBJECTIVES:

Geometry is a core part of mathematical education, because it provides a paradigm of rigorous mathematical reasoning. This module equips students with basic knowledge and skills of euclidean geometry. It thereby prepares the student for the study of other areas of mathematics.

## LEARNING OUTCOMES:

Students who successfully complete this module should be able to:

- understand, express and use geometric results;
- carry out geometric constructions;
- determine certain geometric quantities from others;
- use coordinates to solve geometric problems analytically.

## MODULE CONTENT:

- angle, distance, length, area;
- coordinates;
- lines, triangles and circles;
- geometric constructions;
- congruence and similarity.

## PRIME TEXTS:

OSTERMANN, A., WANNER, G. (2012). Geometry by Its History, Springer.

LANG, S., MURROW, G. (1988). Geometry, Springer.

GARDINER, A. D., BRADLEY, C. J. (2005). Plane Euclidean Geometry: Theory and Problems, The United Kingdom Mathematics Trust.

## OTHER RELEVANT TEXTS:

BRUMFIELD, C. F., VANCE, I. E. (1970). Algebra and Geometry for Teachers, Addison-Wesley.

CLARK, D. M. (2012). Euclidean Geometry: A Guided Inquiry Approach, American Mathematical Society.